To compare the numbers [tex]\(-3 \frac{1}{2}\)[/tex] and [tex]\(-3 \frac{4}{5}\)[/tex], it is helpful to first convert these mixed numbers into improper fractions or decimals.
### Converting Mixed Numbers to Decimals
1. Convert [tex]\(-3 \frac{1}{2}\)[/tex]:
[tex]\[
-3 \frac{1}{2} = -3 + (-\frac{1}{2}) = -3 - 0.5 = -3.5
\][/tex]
2. Convert [tex]\(-3 \frac{4}{5}\)[/tex]:
[tex]\[
-3 \frac{4}{5} = -3 + (-\frac{4}{5}) = -3 - 0.8 = -3.8
\][/tex]
### Comparing the Decimals
- We now have the numbers [tex]\( -3.5 \)[/tex] and [tex]\( -3.8 \)[/tex].
- To compare these two numbers, we look at their positions on the number line.
- Since both numbers are negative, the number with a greater absolute value (ignoring the negative sign) is actually smaller.
- [tex]\( -3.5 \)[/tex] is closer to zero than [tex]\( -3.8 \)[/tex].
Thus, [tex]\( -3.5 \)[/tex] is greater than [tex]\( -3.8 \)[/tex].
### Final Comparison
[tex]\[
-3 \frac{1}{2} > -3 \frac{4}{5}
\][/tex]
So, the correct comparison is:
[tex]\[
-3 \frac{1}{2} > -3 \frac{4}{5}
\][/tex]
